Moderator Note: this is a question from the Federal Mathematics Competition 2013.
Good morning, here's another (pretty difficult) mathematical problem... The task may sound a little strange (I'm from Germany), but I hope you don't mind :)
Anja and Bernd are playing the following game: They alternatingly write down digits on the blackboard. Anja starts. Every additional digit is written down either to the right or to the left of the digits already written on the blackboard. Prove that Anja can prevent the line of digits (including any leading zeros) from representing a square number in the decimal system after any move by Bernd.
Thank you for good answers (at least I hope so)